Final answer:
The GCF of the polynomial 35a^3b^2 - 14a^2b^3 is the highest powers of the common factors in both terms, which is 7a^2b^2, corresponding to option A.
Step-by-step explanation:
The greatest common factor (GCF) of the polynomial 35a3b2 - 14a2b3 can be found by identifying the highest powers of the common factors in both terms.
We look for the greatest coefficient and the highest powers of a and b that can divide both terms of the polynomial without leaving a remainder.
Both terms have factors of 7, a, and b.
The coefficient 7 divides both 35 and 14.
The smallest power of a that appears in both terms is a2, and the smallest power of b is b2.
Therefore, the GCF is 7a2b2.
This corresponds to option A.